Distorted mesh when I use a bevel object on Nurbs curve vs. Bezier curve
Your bezier curve based balloon object does not have its scale applied, it scaled 0.25 on all axis, that is why the bevel is not at its true size compared to the bevel object. The NURBS based one is the correct one here.

If you do apply the scale Blender will try to compensate automatically by changing vertex bevel radius to keep the same size so applying scale alone won't fix your issue.

You then have to enter Edit Mode, select all curve vertex and explicitly set the bevel radius back to 1 as described in my answer

A a side note, also have in mind that your NURBS curve made from many points is too dense, and will invariably lead to self intersections and rendering and display artifacts caused by the large bevel section relative to point density.

It will also lead to an unnecessarily heavy geometry which is too dense with no discernible advantage. I'd strongly advise severe cleanup or using a cleaner modelling method. See my answer about cleaning up curves for some tips